Treffer: Some Properties of Nonstar Steps in Addition Chains and New Cases Where the Scholz Conjecture Is True: Some properties of nonstar steps in addition chains and new cases where the Scholz conjecture is true
Title:
Some Properties of Nonstar Steps in Addition Chains and New Cases Where the Scholz Conjecture Is True: Some properties of nonstar steps in addition chains and new cases where the Scholz conjecture is true
Authors:
Source:
Journal of Algorithms. 42:304-316
Publisher Information:
Elsevier BV, 2002.
Publication Year:
2002
Subject Terms:
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
0196-6774
DOI:
10.1006/jagm.2002.1212
Access URL:
Rights:
Elsevier TDM
Accession Number:
edsair.doi.dedup.....d2c933a586e15db0682a7ce9405e206b
Database:
OpenAIRE
Weitere Informationen
Summary: Let \(\ell(n)\) be the smallest possible length of addition chains for a positive integer \(n\). Then A. Scholz (1937) conjectured that \(\ell(2^n-1)\leq n+\ell(n)-1\), which still remains open. It is known that the Scholz conjecture is true when \(\nu(n)\leq 4\), where \(\nu(n)\) is the number of 1's in the binary representation of \(n\). In this paper, we give some properties of nonstar steps in addition chains and prove that the Scholz conjecture is true for infinitely many new integers including the case where \(\nu(n)= 5\).